A Three-Way Decision Model Based on Intuitionistic Fuzzy Decision Systems

Liu, Jiubing; Zhou, Xianzhong; Huang, Bing; Li, Huaxiong

doi:10.1007/978-3-319-60840-2_18

Cited by 11 publications

(7 citation statements)

References 30 publications

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“…Let P(Γ | [x]) be the conditional probability that x belongs to Γ, and P(¬Γ | [x]) is the conditional probability that x belongs to ¬Γ. erefore, we can get P( [24,33,34], for the matter x, the expected losses R(a i | [x])(i � P, B, N) from taking different operations are indicated as follows:…”

Section: Basic Model Of Svndtrsmentioning

confidence: 99%

“…In the 3WD model, the loss function (LF) is a key parameter. e scholars have studied a great deal of 3WD rules based on LFs of diverse forms, such as interval number [23], IFSs [24], intuitionistic uncertain linguistic variables [25], dual hesitant FSs [26], and Pythagorean FSs [27]. SVNS can handle uncertain, incomplete, and inconsistent information more flexibly.…”

Section: Introductionmentioning

confidence: 99%

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Three‐Way Decisions with Single‐Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis

Лю

Yang

2019

Mathematical Problems in Engineering

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The single-valued neutrosophic set (SVNS) can not only depict imperfect information in the real decision system but also handle undetermined and inconformity information flexibly and effectively. Three-way decisions (3WDs) are often used as an effective method to deal with uncertainties, but the conditional probability is given by the decision maker subjectively, which makes the decision result too subjective. This paper proposes a novel model based on 3WDs to settle the multiattribute decision-making (MADM) problems, where the attribute values are described by SVNS, and the attribute weights are entirely unknown. At first, we build a single-valued neutrosophic decision theory rough set (SVNDTRS) model based on Bayesian decision process. Then, we use the analytic hierarchy process (AHP) approach to calculate the subjective weight of each attribute, the information entropy to obtain the attribute’s objective weight, and the minimum total deviation approach to determine the combined weight of the attributes. After obtaining the standard weight, the grey relational analysis (GRA) method is utilized to calculate the grey correlation closeness with the ideal solution, and the conditional probability is estimated by it. In addition, we develop a decision-making method in view of the ideal solution of 3WDs with the SVNS. This approach not only considers the lowest cost but also gives a corresponding semantic explanation for the decision result of each alternative, which can supplement the decision results of GRA. At last, we illustrate the feasibility and effectiveness of 3WDs through an example of supplier selection and compare it with other methods to verify the advantages of our approach.

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Section: Basic Model Of Svndtrsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three‐Way Decisions with Single‐Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis

Лю

Yang

2019

Mathematical Problems in Engineering

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“…Wang et al [16,17] predicted the seasonal fluctuations of the electricity consumption and the quarterly hydropower production in China. Li et al [18] proposed the GM(1,1) predictive model, which realized the prediction of the intuitive fuzzy number. Wang et al [19] proposed a new gray model based on data grouping and buffer operator, and the model groups on a monthly or quarterly basis are grouped, which are then buffered separately to cope with prediction error caused by seasonal fluctuations and sudden changes in trend.…”

Section: Introductionmentioning

confidence: 99%

Model of Automobile Parts Sale Prediction Based on Nonlinear Periodic Gray GM(1,1) and Empirical Research

Gong

Wang²

2019

Mathematical Problems in Engineering

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The traditional predictive method cannot fully reflect the complex nonlinear characteristics and regularities of automobile and parts sales data, so the prediction precision is not high. The purpose of this paper is to propose the gray GM(1,1) nonlinear periodic predictive model by introducing the seasonal variation index to improve predictive accuracy of the single GM(1,1) model. Firstly, the paper analyzes concept of GM(1,1) and then proposes the gray GM(1,1) nonlinear periodic predictive model to forecast automobile parts sales. The model algorithm used gray theory and accumulated technology to generate new data and set up unified differential equations to find the fitting curve of automobile parts sales prediction by the seasonal variation index to remove random elements. Lastly, the gray GM(1,1) nonlinear periodic predictive model is used for empirical analysis; the result of example shows that the model proposed in the paper is feasible. The superiority of the proposed predictive model compared with the single gray GM(1,1) model is demonstrated. The reliability of this model is experienced by the accuracy test, which provides a theoretical guidance for the prediction of automobile part sales. And the average relative error is reduced by 8.52% compared with the single GM(1,1) model.

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“…Yang et al combined three-way decisions theory with IFS to obtain novel three-way decision rules [38]. At the same time, Liu et al explored the intuitionistic fuzzy three-way decision theory based on intuitionistic fuzzy decision systems [39]. Nevertheless, Yang et al [38] and Liu et al [39] only considered the case of a single granularity, and did not analyze the decision-making situation of multiple granularities in an intuitionistic fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, Liu et al explored the intuitionistic fuzzy three-way decision theory based on intuitionistic fuzzy decision systems [39]. Nevertheless, Yang et al [38] and Liu et al [39] only considered the case of a single granularity, and did not analyze the decision-making situation of multiple granularities in an intuitionistic fuzzy environment. The DTRS and three-way decisions theory are both used to deal with decision-making problems, so it is also enlightening for us to study three-way decisions theory through DTRS.…”

Section: Introductionmentioning

confidence: 99%

Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

Xue

Han

et al. 2018

Symmetry

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The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities.

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A Three-Way Decision Model Based on Intuitionistic Fuzzy Decision Systems

Cited by 11 publications

References 30 publications

Three‐Way Decisions with Single‐Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis

Three‐Way Decisions with Single‐Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis

Model of Automobile Parts Sale Prediction Based on Nonlinear Periodic Gray GM(1,1) and Empirical Research

Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

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